%0 Journal Article %J Applied Mathematics %D 2012 %T The H-Decomposition Problem for Graphs %A Sousa, Teresa %N 11 %P 1719-1722 %U http://www.scirp.org/journal/am/ %V 3 %X

The concept of H-decompositions of graphs was first introduced by Erdös, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decompositions of graphs.

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